Find u(t,x) solving the IVP on the half-line for the diffusion equation:

ut - uxx = 0 (t>0; x in R)
ux(t,0) = sin(t)
u(0,x) = x

I can do this problem for the most part but I'm struggling to get rid of the non-zero Neumann boundary condition. (I know the heat kernel/fundamental solution and odd/even reflection technique).

Question

01-08-2017
Mathematics

contestada

Find u(t,x) solving the IVP on the half-line for the diffusion equation:

ut - uxx = 0 (t>0; x in R)
ux(t,0) = sin(t)
u(0,x) = x

I can do this problem for the most part but I'm struggling to get rid of the non-zero Neumann boundary condition. (I know the heat kernel/fundamental solution and odd/even reflection technique).

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